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Atholl Anderson has long been interested in the big questions surrounding pre-European population movement in the Asia-Pacific. For the most part, though, his publications have concentrated on the initial settlement of Remote Oceania, and particularly Polynesia, rather than either the Austronesian progression through Southeast Asia or the Lapita spread through Near Oceania. In this chapter, I would like to return to his 2001 consideration of Lapita mobility, where he asked (Anderson 2001:21) whether the large-scale pattern of episodic movement he identified in Remote Oceania could be linked at a processual level with the Lapita spread through already-inhabited parts of Melanesia and preceding population movements in Asia. I have two aims in addressing this question. The first is to begin to explore the potential of a new way of characterising and explaining the Lapita phenomenon. My focus is on a type of episodic movement known as a ‘Lévy flight’. My second aim is to consider whether the patterns and processes I discuss in this connection can be meshed with Anderson’s models concerning punctuated or episodic colonisation. The objective is to help test the processual links he proposes between varying patterns or cycles of mobility stretching all the way from South China to South Polynesia. I am particularly interested to know whether the presence of existing populations in northwestern Melanesia really made any difference to the process underlying the large-scale, long-term movement of people that eventually saw the colonisation of Remote Oceania, or whether there is, to put it in Anderson’s words (2001:21), ‘an inherent trajectory in island colonisation which is ... self-sufficient in its processes and causes and which, if all islands were the same, would display a regular pattern of binary mobility phases?’.

Flights of fancy: Fractal geometry, the Lapita dispersal and punctuated colonisation in the Pacific